We analyze the performance of a ferroelectric liquid crystal on silicon display (FLCoS) as a binary polarization diffraction grating. We analyze the correspondence between the two polarization states emerging from the displayed grating and the polarization and intensity of the diffracted orders generated at the Fourier diffraction plane. This polarization-diffraction analysis leads, in a simple manner, to configurations yielding binary amplitude or binary phase modulation by incorporating an analyzer on the reflected beam. Based on this analysis, we present two useful variations of the polarization configuration. The first is a simplification using a single polarizer, which provides equivalent results for amplitude or phase modulation as the more general operational mode involving two polarizers. The second variation is proposed to compensate the reduction of the diffraction efficiency when the operating wavelength differs from the design one (for which the FLCoS liquid-crystal layer acts as a half-wave plate). In this situation we show how the ideal grating performance can be recovered in spite of the phase-shift mismatch originated by chromatic dispersion. In all cases, we provide experimental results that verify the theoretical analyses.